双参保守复混沌系统的构建及偏置增压控制

Construction of a conservative complex chaotic system with double parameters and biased boosting control

基于经典保守混沌系统的结构,构造了一个双参数保守混沌系统,能够产生复杂动力学现象。通过理论分析和多种数值仿真方法,研究了系统结构参数和外力参数对混沌性、保守性、平衡状态和稳定性的影响。结果表明,随着参数的变化,系统相体积保持守恒,呈现混沌、周期运动等现象,并证明了参数对平衡状态的影响。此外,通过虚实分离的方法构造了复系统,并研究了其动力学特性,发现实混沌系统所构造的复系统中,同样具有混沌性和保守性,且具有大参数范围混沌现象。设计了控制器,使系统产生偏置增压现象,并可对信号极性进行控制。最后,设计了系统电路并进行了仿真,结果与理论相符,证明了混沌系统的物理可行性。

Based on the structure of a classic conservative chaotic system,this paper builds a double-parameter conservative chaotic system capable of generating complex dynamic phenomena.Through theoretical analysis and various numerical simulation methods,the effects of system structural parameters and external force parameters on chaos,conservativeness,equilibrium states,and stability are investigated.Our results indicate with the variations of the parameters,the phase volume of the system remains constant and exhibits chaotic and periodic motion,confirming the impact of parameters on equilibrium states.Additionally,a complex system is built by employing the virtual-physical separation,and its dynamical characteristics are investigated.Our results show the complex system built on a real chaotic system also exhibits chaotic and conservative properties and shows chaos over a wide range of parameter values.A controller is designed to induce biased perturbation in the system and control signal polarity.Finally,the system circuit is designed and simulated,yielding results in conformity with theoretical calculations,demonstrating the physical feasibility of the chaotic system.